2. The box plot shows the times, $t$ minutes, it takes a group of office workers to travel to work.\\
\includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-04_365_1237_351_356}
\begin{enumerate}[label=(\alph*)]
\item Find the range of the times.
\item Find the interquartile range of the times.
\item Using the quartiles, describe the skewness of these data. Give a reason for your answer.

Chetna believes that house prices will be higher if the time to travel to work is shorter. She asks a random sample of these office workers for their house prices $\pounds x$, where $x$ is measured in thousands, and obtains the following statistics

$$\mathrm { S } _ { x x } = 5514 \quad \mathrm {~S} _ { x t } = 10 \quad \mathrm {~S} _ { t t } = 1145.6$$
\item Calculate the product moment correlation coefficient between $x$ and $t$.
\item State, giving a reason, whether or not your correlation coefficient supports Chetna's belief.

Adam and Betty are part of the group of office workers and they have both moved house. Adam's time to travel to work changes from 32 minutes to 36 minutes. Betty's time to travel to work changes from 38 minutes to 58 minutes. Outliers are defined as values that are more than 1.5 times the interquartile range above the upper quartile.
\item Showing all necessary calculations, determine how the box plot of times to travel to work will change and draw a new box plot on the grid on page 5.

\includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-05_499_1413_2122_180}
\end{enumerate}

\hfill \mbox{\textit{Edexcel S1 2017 Q2 [11]}}